Haralick texture features

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Haralick's texture features [28] were calculated using
the kharalick() function of the cytometry tool box
[29] for Khoros (version 2.1 Pro, Khoral Research,
Inc., Albuquerque, NM USA; http://www.khoral.com). The basis
for these features is the gray-level co-occurrence matrix
(>>>>
G in Equation 2.6). This matrix is square
with dimension >>>>Ng, where >>>>Ng is the number of gray levels in the
image. Element >>>>[i,j] of the matrix is generated by counting the
number of times a pixel with value >>>>i is adjacent to a pixel with
value >>>>j and then dividing the entire matrix by the total number of
such comparisons made. Each entry is therefore considered to be the
probability that a pixel with value >>>>i will be found adjacent to a
pixel of value >>>>j.
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(2.6)

Since adjacency can be defined to occur in each of four directions in
a 2D, square pixel image (horizontal, vertical, left and right
diagonals - see Figure 2.2), four such
matrices can be calculated.
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Figure 2.2:
Four directions of
adjacency as defined for calculation of the Haralick texture
features. The Haralick statistics are calculated for co-occurrence
matrices generated using each of these directions of adjacency.

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Zernike moments through degree 12 were calculated (>>>>Znl such that
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in Equation 2.4) using the code in
Section 5.2.1 (p. ).
Since the moments themselves are complex numbers and are sensitive to
rotation of the image, the magnitudes of the moments were used as
features (i.e. >>>>|Znl|) [21]. This provided 49
descriptive features for each image.
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Haralick then described 14 statistics that can be calculated from the
co-occurrence matrix with the intent of describing the texture of the
image:
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Since rotation invariance is a primary criterion for any features used
with these images, a kind of invariance was achieved for each of these
statistics by averaging them over the four directional co-occurrence
matrices. The maximal correlation coefficient was not calculated due
to computational instability so there were 13 texture features for
each image.
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